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Chapter 0: Problem 97

Simplify the expressions in Exercises \(97-106 .\) $$ 4^{-1 / 2} 4^{7 / 2} $$

Short Answer

Expert verified
The simplified expression for \( 4^{-1/2} 4^{7/2} \) is 64.

Step by step solution

01

Apply the Product Rule for Exponents

Let's apply the product rule to the given expressions by adding their exponents: \( 4^{-1/2} 4^{7/2} = 4^{-1/2 + 7/2} \)
02

Combine the Exponents

Now, we'll combine the exponents by adding the fractions: \[ -\frac{1}{2} + \frac{7}{2} = \frac{-1 + 7}{2} = \frac{6}{2} \] So, the combined expression becomes: \[ 4^{\frac{6}{2}} \]
03

Simplify the Expression

Lastly, we'll simplify the exponent: \[ \frac{6}{2} = 3 \] So, the simplified expression is: \[ 4^3 \]
04

Evaluate the Expression

Finally, let's evaluate the expression by raising 4 to the power of 3: \[ 4^3 = 4 \times 4 \times 4 = 64 \] So, the simplified expression is 64.

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Most popular questions from this chapter

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(\left(2-5^{\star}(-1)\right) / 1-2 *(-1)\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(2 \cdot(-1)^{2} / 2\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(\frac{1+4}{100}\right)^{-3}\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(2 x^{2}+7 x-4=0\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{2}-x+1=0\)
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